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PROFESSOR O. REYNOLDS ON THE THEORY OF LUBRICATION 
Section III.— General View of the Action of Lubrication. 
14. The case of two nearly parallel Surfaces separated by a viscous Fluid. 
Let AB and CD (fig. 4) be perpendicular sections of the surfaces, CD being of 
limited but great extent compared with the distance h between the surfaces, both 
surfaces being of unlimited length in a direction perpendicular to the paper. 
Fig. 4. 
Case 1 . Parallel Surfaces in Relative Tangential Motion. —In fig. 5 the surface CD 
is supposed fixed, while AB moves to the left with a velocity U. 
Then by the definition of viscosity (Art. 9) there will be a tangential resistance 
and the tangential motion of the fluid will vary uniformly from U at AB to zero at 
CD. Thus if FG (fig. 5) be taken to represent U, then PN will represent the velocity 
in the fluid at P. 
The slope of the line EG therefore may be taken to represent the force F, and the 
direction of the tangential force on either surface is the same as if EG were in tension. 
The sloping lines therefore represent the condition of motion and stress throughout 
the film (fig. 5). 
Fig. 5. 
Case 2. Parallel Surfaces approaching with no Tangential Motion. —The fluid has 
to be scpieezed out between the surfaces, and since there is no motion at the surface, 
the horizontal velocity outward will be greatest half-way between the surfaces, 
nothing at O the middle of CD, and greatest at the ends. 
If in a certain state of the motion (shown by dotted line, fig. 6) the space between 
AB and CD be divided into 10 equal parts by vertical lines (fig. 6, dotted figure), and 
these lines supposed to move with the fluid, they will shortly after assume the positions 
